Theorems · Theorem · combinatorics
Graph.IsInducedSubgraph.isLink_of_mem_mem
∀ {α : Type u_1} {β : Type u_2} {H G : Graph α β},
H.IsInducedSubgraph G → ∀ ⦃e : β⦄ ⦃x y : α⦄, G.IsLink e x y → x ∈ H.vertexSet → y ∈ H.vertexSet → H.IsLink e x y- Defined in
- Mathlib.Combinatorics.Graph.Subgraph
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Graphstatement and proof · cited by 242
- Graph.IsLinkstatement · cited by 124
- Graph.vertexSetstatement · cited by 87
- Graph.IsInducedSubgraphstatement and proof · cited by 16
Cited by8
Results whose statement or proof uses this declaration.
- Graph.IsInducedSubgraph.not_isClosedSubgraph_iff_exists_adjproof · cited by 1
- Graph.IsInducedSubgraph.isLink_congrproof · cited by 0
- Graph.IsInducedSubgraph.le_of_le_subsetproof · cited by 0
- Graph.IsInducedSubgraph.transproof · cited by 0
- Graph.IsSubgraph.not_isInducedSubgraph_iffproof · cited by 0
- Graph.IsInducedSubgraph.adj_congrproof · cited by 0
- Graph.IsInducedSubgraph.anti_rightproof · cited by 0
- Graph.IsInducedSubgraph.ext_of_vertexSetproof · cited by 0